Read and state three-figure bearings

How is a true bearing measured?

A forward direction turns steadily from 170° through 180° to 190°. What do you predict for its reverse direction?

The solid ray shows the forward direction; the dashed ray shows the reverse direction from the same centre. Move the forward angle from 170 to 190 degrees. Watch the dashed ray pass north and compare its angle readout

What happens as the reverse ray passes north?

Use north and a clockwise turn

A bearing describes a direction within one full turn. Write it with three digits. Reversing a direction makes a half-turn

1. 1Locate the cardinal directions Use these as reference directions when the marked angle starts elsewhere \(\displaystyle \begin{aligned}N&=000^{\circ}\\E&=090^{\circ}\\S&=180^{\circ}\\W&=270^{\circ}\end{aligned}\)
2. 2Use three digits Add leading zeros when needed. North is written with three zeros \(\displaystyle \begin{aligned}7^{\circ}&\longrightarrow007^{\circ}\\43^{\circ}&\longrightarrow043^{\circ}\end{aligned}\)
3. 3Reverse a direction Add a half-turn below south's bearing. Otherwise subtract a half-turn \(\displaystyle \begin{aligned}078^{\circ}+180^{\circ}&=258^{\circ}\\286^{\circ}-180^{\circ}&=106^{\circ}\end{aligned}\)
4. 4Follow a turn Add a clockwise turn or subtract an anticlockwise turn. Remove or add a full turn if the result lies outside the bearing range \(\displaystyle 0^{\circ}\leq b<360^{\circ}\)

Direction information

\(\displaystyle \alpha=7^{\circ}\)

A ray points seven degrees clockwise from true north. Write its three-figure bearing

Direction information

\(\displaystyle b=0^{\circ}\)

A ray points due north. Use this topic’s range from 0° inclusive to 360° exclusive. Write its three-figure bearing

State the three-figure bearing of B from A. The diagram is not to scale

Start from west's bearing. The ray lies towards south. Write exactly three digits, including leading zeros when needed

Bearing of B from A

\(\displaystyle 064^{\circ}\)

Find the three-figure bearing of A from B.

The return direction is a half-turn from the outward direction. Write exactly three digits, including leading zeros when needed

Bearing of D from C

\(\displaystyle 293^{\circ}\)

Find the three-figure bearing of C from D.

Choose the half-turn that leaves a value within one full turn. Write exactly three digits, including leading zeros when needed

Bearing of Q from P

\(\displaystyle 317^{\circ}\)

Clockwise turn from the forward direction at Q

\(\displaystyle 58^{\circ}\)

At Q the route turns clockwise and continues to R. Find the three-figure bearing of R from Q

Continue the forward direction at Q before applying the turn. Pass north if necessary. Write exactly three digits, including leading zeros when needed

Direction information

\(\displaystyle \begin{aligned}b_{PQ}&=020^{\circ}\\\text{anticlockwise turn}&=35^{\circ}\end{aligned}\)

A route arrives at Q travelling on bearing 020°, then turns 35° anticlockwise towards R. Find the bearing of Q from R

A handheld compass reports a magnetic bearing. Can it automatically be used as a true bearing in a map problem?

Direction of B from A, anticlockwise from north

\(\displaystyle 24^{\circ}\)

A student finds the return bearing. Which line is the first error?